The idea is to group voters by ballot type (or latent preference but that’s not observable), and then view the issue of participation as an adversarial game among those groups.

As a strategy, each group chooses how many of their ballots to cast (and how many to abstain). In a more complicated scenario, the groups could also choose how to distribute the ballots they cast among the other ballot types, but that’s probably too much.

This is a large game but it’s finite, so it has a Nash equilibrium over mixed strategies. Any equilibrium induces a lottery over decisions.

In principle, this is something that could be simulated. Say as a big ask that group utility functions were set up normatively or faithfully enough. Then under certain assumptions, a method that simulated the equilibrium strategies over groups would “essentially” satisfy participation, since casting a ballot would only give one’s group an extra pure strategy to sample from.

Roughly, I’m considering whether the no-show/abstention problem can be all but artificially removed under certain assumptions about group utility functions, and whether those assumptions are reasonable enough or not.

It could be that there is some recursive issue of meta participation. In fact, I think that even casting a ballot and allowing it to be a strategic option for one’s group can change the game globally as other groups adjust, which may mean the problem persists unless perhaps other conditions are met… In a zero-sum situation, I don’t think increased optionality can reduce the equilibrium payoff for a group.